We simulated antagonistic population dynamics using a discrete Lotka-Volterra competition model, where each population’s growth rate is influenced by the fluctuations in a competitor population. Pairs of populations were simulated according to:
\[\begin{equation} N_i(t+1) = N_i(t) + \lambda_i * N_i(t) \end{equation}\]where \(N_i\) is the size of population \(i\), \(t\) is each time step, and \(\lambda\) is the true growth rate of population \(i\). The true growth rate (\(\lambda\)) is determined by:
\[\begin{equation} \lambda_i = r*(1-\frac{(N_i(t) + \alpha_{ji}N_j(t))}{K_i}) \end{equation}\]where \(r\) is population \(i\)’s maximum growth rate, \(\alpha_{ji}\) is the interaction effect of population \(j\) on population \(i\), \(N_j\) is the size of population \(j\), and \(K_i\) is the carrying capacity of population \(i\).
To test index sensitivity to error, we introduced process and observation error into the generated population time series.
| Value | |
|---|---|
| Number of population pairs | 10.0 |
| Time steps | 10.0 |
| Initial size (N0) | 100.0 |
| Maximum growth rate (r) | 1.5 |
To test index sensitivity to direction of change, we generated three scenarios of population-level biodiversity change.
We varied carrying capacity through time to drive populations to:
In each scenario, carrying capacity begins at \(K = 100\) and each population’s initial size is exactly at this carrying capacity (\(N_0 = 100\)).
Figure 1: Carrying capacity trends used to generate the biodiversity change scenarios.
To test whether the LPI is sensitive to lags in the covariance between populations, we then generated two levels of lag in the interaction effect dictating how populations covary through time:
For each biodiversity change scenario, index sensitivity was measured as the accuracy and precision of the calculated Living Planet Index when compared to the true biodiversity change trend. This true LPI trend was obtained by calculating the index values through time based on a population generated from the same parameters we used to generate populations for each scenario, without any added process error.
We measured accuracy as the difference between the calculated LPI and true LPI trend at each time step:
\[accuracy = LPI_{calculated} - LPI_{true}\]
As a first metric of precision, we evaluated whether the true LPI trend fell within the 95% confidence interval around the calculated LPI trend obtained from bootstrap resampling at each time step. As a second precision metric, we measured precision as the difference between the expected uncertainty interval and the width of the 95% confidence interval. The expected uncertainty interval is determined based on the process and observation errors introduced into the simulated population trends. I calculated each population’s growth rate with and without introduced error, and took the difference between the two to get a measure of the total introduced uncertainty in the growth rates. Then, I converted this uncertainty to the same scale as the LPI:
\[ precision = LPI_{CIwidth} - LPI_{uncertainty} \]
| i | j | |
|---|---|---|
| Interaction effect (alpha) | 0 | 0 |
| Observation error | +/- 5 | +/- 5 |
| Process error | +/- 0, 0.1, 0.2 | +/- 0, 0.1, 0.2 |
| Lag | 0 | 0 |
Figure 2: True and calculated LPI trends for each direction of biodiversity change.
Figure 3: True and calculated LPI trends for each direction of biodiversity change.
Figure 4: True and calculated LPI trends for each direction of biodiversity change.
Figure 5: LPI sensitivity to direction of change.
Figure 6: LPI sensitivity to direction of change.
Figure 7: LPI sensitivity to direction of change.
| direction | Process_error | mean_accuracy | mean_precision |
|---|---|---|---|
| decline | 0 | -0.01 | -0.213 |
| decline | 0.1 | 0.00 | -0.222 |
| decline | 0.2 | 0.00 | -0.221 |
| stable | 0 | -0.01 | -0.216 |
| stable | 0.1 | 0.00 | -0.224 |
| stable | 0.2 | 0.00 | -0.224 |
| growth | 0 | -0.02 | -0.221 |
| growth | 0.1 | -0.01 | -0.226 |
| growth | 0.2 | -0.01 | -0.232 |
Figure 8: Ability to capture the true LPI
| direction | Process_error | true_within_rlpiCI | n | perc |
|---|---|---|---|---|
| decline | 0 | Success | 11 | 1.0000000 |
| decline | 0.1 | Success | 11 | 1.0000000 |
| decline | 0.2 | Success | 11 | 1.0000000 |
| stable | 0 | Success | 10 | 0.9090909 |
| stable | 0.1 | Success | 11 | 1.0000000 |
| stable | 0.2 | Success | 11 | 1.0000000 |
| growth | 0 | Success | 4 | 0.3636364 |
| growth | 0.1 | Success | 4 | 0.3636364 |
| growth | 0.2 | Success | 9 | 0.8181818 |
Figure 9: Ability to capture the true LPI
To test whether the LPI is sensitive to covariance between populations, we generated biodiversity change scenarios with two types of interaction effects (\(\alpha\)) between populations:
Each type of interaction was tested at two interaction strengths. All interaction effects were immediate, meaning there was no time lag in the covariance in the populations’ growth rates.
| i | j | |
|---|---|---|
| Interaction effect (alpha) | 0 | 0 |
| Observation error | +/- 5 | +/- 5 |
| Process error | +/- 0, 0.1, 0.2 | +/- 0, 0.1, 0.2 |
| Lag | 0 | 0 |
Figure 10: True and calculated LPI trends for each scenario.
Figure 11: True and calculated LPI trends for each scenario.
Figure 12: True and calculated LPI trends for each scenario.
Figure 13: LPI sensitivity to direction of change and covariance.
Figure 14: LPI sensitivity to direction of change and covariance.
Figure 15: LPI sensitivity to direction of change and covariance.
| direction | interaction | mean_accuracy | se_accuracy | mean_precision | se_precision |
|---|---|---|---|---|---|
| decline | Strong Asynchrony | -0.004 | 0.001 | -0.357 | 0.039 |
| decline | Weak Asynchrony | -0.016 | 0.002 | -0.257 | 0.030 |
| decline | No Synchrony | -0.006 | 0.002 | -0.213 | 0.026 |
| decline | Weak Synchrony | -0.009 | 0.001 | -0.208 | 0.025 |
| decline | Strong Synchrony | -0.009 | 0.001 | -0.206 | 0.025 |
| stable | Strong Asynchrony | -0.018 | 0.003 | -0.346 | 0.038 |
| stable | Weak Asynchrony | -0.024 | 0.003 | -0.250 | 0.029 |
| stable | No Synchrony | -0.010 | 0.002 | -0.216 | 0.026 |
| stable | Weak Synchrony | -0.014 | 0.002 | -0.206 | 0.025 |
| stable | Strong Synchrony | -0.015 | 0.002 | -0.205 | 0.025 |
| growth | Strong Asynchrony | -0.030 | 0.004 | -0.335 | 0.037 |
| growth | Weak Asynchrony | -0.029 | 0.004 | -0.259 | 0.030 |
| growth | No Synchrony | -0.023 | 0.003 | -0.221 | 0.027 |
| growth | Weak Synchrony | -0.012 | 0.002 | -0.215 | 0.026 |
| growth | Strong Synchrony | -0.011 | 0.002 | -0.215 | 0.026 |
Figure 16: Ability to capture the true LPI
| direction | interaction | Process_error | true_within_rlpiCI | n | perc |
|---|---|---|---|---|---|
| decline | Strong Asynchrony | 0 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 0 | Success | 4 | 0.3636364 |
| decline | Weak Asynchrony | 0.1 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 0.2 | Success | 11 | 1.0000000 |
| decline | No Synchrony | 0 | Success | 11 | 1.0000000 |
| decline | No Synchrony | 0.1 | Success | 11 | 1.0000000 |
| decline | No Synchrony | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 0 | Success | 7 | 0.6363636 |
| decline | Weak Synchrony | 0.1 | Success | 8 | 0.7272727 |
| decline | Weak Synchrony | 0.2 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 0 | Success | 8 | 0.7272727 |
| decline | Strong Synchrony | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 0 | Success | 4 | 0.3636364 |
| stable | Strong Asynchrony | 0.1 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 0 | Success | 3 | 0.2727273 |
| stable | Weak Asynchrony | 0.1 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 0.2 | Success | 11 | 1.0000000 |
| stable | No Synchrony | 0 | Success | 10 | 0.9090909 |
| stable | No Synchrony | 0.1 | Success | 11 | 1.0000000 |
| stable | No Synchrony | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Synchrony | 0 | Success | 6 | 0.5454545 |
| stable | Weak Synchrony | 0.1 | Success | 7 | 0.6363636 |
| stable | Weak Synchrony | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Synchrony | 0 | Success | 6 | 0.5454545 |
| stable | Strong Synchrony | 0.1 | Success | 8 | 0.7272727 |
| stable | Strong Synchrony | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 0 | Success | 4 | 0.3636364 |
| growth | Strong Asynchrony | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 0.2 | Success | 11 | 1.0000000 |
| growth | Weak Asynchrony | 0 | Success | 3 | 0.2727273 |
| growth | Weak Asynchrony | 0.1 | Success | 9 | 0.8181818 |
| growth | Weak Asynchrony | 0.2 | Success | 7 | 0.6363636 |
| growth | No Synchrony | 0 | Success | 4 | 0.3636364 |
| growth | No Synchrony | 0.1 | Success | 4 | 0.3636364 |
| growth | No Synchrony | 0.2 | Success | 9 | 0.8181818 |
| growth | Weak Synchrony | 0 | Success | 8 | 0.7272727 |
| growth | Weak Synchrony | 0.1 | Success | 10 | 0.9090909 |
| growth | Weak Synchrony | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 0 | Success | 8 | 0.7272727 |
| growth | Strong Synchrony | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 0.2 | Success | 11 | 1.0000000 |
The LPI is sensitive to covariance when trends are declining:
* The LPI is particularly sensitive to negative covariance in declining trends, which are very overestimated (alpha = 0.1 and 0.2)
* growing and stable trends are slightly overestimated when there is high positive covariance
* however, this sensitivity does not change at different levels of process error
We introduced two levels of lag in the interaction effect that influences how populations covary through time:
Both of these lags were introduced into positively and negatively covarying populations shown above.
| i | j | |
|---|---|---|
| Interaction effect (alpha) | 0 | 0 |
| Observation error | +/- 5 | +/- 5 |
| Process error | +/- 0, 0.1, 0.2 | +/- 0, 0.1, 0.2 |
| Lag | 0, 1, 2 | 0, 1, 2 |
The LPI is not sensitive to lags of 1 or 2 time steps.
| direction | interaction | Lag | Process_error | mean_accuracy | se_accuracy | mean_precision | se_precision |
|---|---|---|---|---|---|---|---|
| decline | Strong Asynchrony | 0 | 0 | -0.004 | 0.001 | -0.357 | 0.039 |
| decline | Strong Asynchrony | 0 | 0.1 | -0.006 | 0.001 | -0.307 | 0.038 |
| decline | Strong Asynchrony | 0 | 0.2 | -0.008 | 0.001 | -0.406 | 0.056 |
| decline | Strong Asynchrony | 1 | 0 | -0.002 | 0.000 | -0.368 | 0.049 |
| decline | Strong Asynchrony | 1 | 0.1 | -0.004 | 0.001 | -0.422 | 0.053 |
| decline | Strong Asynchrony | 1 | 0.2 | -0.007 | 0.001 | -0.502 | 0.072 |
| decline | Strong Asynchrony | 2 | 0 | -0.002 | 0.000 | -0.355 | 0.039 |
| decline | Strong Asynchrony | 2 | 0.1 | 0.006 | 0.001 | -0.392 | 0.047 |
| decline | Strong Asynchrony | 2 | 0.2 | 0.006 | 0.002 | -0.506 | 0.065 |
| decline | Weak Asynchrony | 0 | 0 | -0.016 | 0.002 | -0.257 | 0.030 |
| decline | Weak Asynchrony | 0 | 0.1 | -0.005 | 0.001 | -0.194 | 0.025 |
| decline | Weak Asynchrony | 0 | 0.2 | -0.003 | 0.001 | -0.214 | 0.029 |
| decline | Weak Asynchrony | 1 | 0 | -0.007 | 0.001 | -0.258 | 0.032 |
| decline | Weak Asynchrony | 1 | 0.1 | -0.005 | 0.001 | -0.297 | 0.034 |
| decline | Weak Asynchrony | 1 | 0.2 | -0.007 | 0.001 | -0.322 | 0.038 |
| decline | Weak Asynchrony | 2 | 0 | -0.009 | 0.001 | -0.254 | 0.029 |
| decline | Weak Asynchrony | 2 | 0.1 | 0.001 | 0.001 | -0.257 | 0.031 |
| decline | Weak Asynchrony | 2 | 0.2 | 0.001 | 0.000 | -0.295 | 0.036 |
| decline | Weak Synchrony | 0 | 0 | -0.009 | 0.001 | -0.208 | 0.025 |
| decline | Weak Synchrony | 0 | 0.1 | -0.005 | 0.001 | -0.218 | 0.027 |
| decline | Weak Synchrony | 0 | 0.2 | -0.004 | 0.001 | -0.241 | 0.031 |
| decline | Weak Synchrony | 1 | 0 | -0.007 | 0.001 | -0.214 | 0.026 |
| decline | Weak Synchrony | 1 | 0.1 | -0.002 | 0.001 | -0.221 | 0.028 |
| decline | Weak Synchrony | 1 | 0.2 | 0.001 | 0.000 | -0.259 | 0.030 |
| decline | Weak Synchrony | 2 | 0 | -0.008 | 0.001 | -0.209 | 0.025 |
| decline | Weak Synchrony | 2 | 0.1 | -0.002 | 0.001 | -0.184 | 0.021 |
| decline | Weak Synchrony | 2 | 0.2 | -0.003 | 0.001 | -0.205 | 0.025 |
| decline | Strong Synchrony | 0 | 0 | -0.009 | 0.001 | -0.206 | 0.025 |
| decline | Strong Synchrony | 0 | 0.1 | -0.003 | 0.000 | -0.391 | 0.060 |
| decline | Strong Synchrony | 0 | 0.2 | -0.004 | 0.001 | -0.611 | 0.093 |
| decline | Strong Synchrony | 1 | 0 | -0.004 | 0.001 | -0.256 | 0.031 |
| decline | Strong Synchrony | 1 | 0.1 | -0.004 | 0.001 | -0.419 | 0.058 |
| decline | Strong Synchrony | 1 | 0.2 | -0.016 | 0.004 | -0.578 | 0.088 |
| decline | Strong Synchrony | 2 | 0 | -0.004 | 0.001 | -0.244 | 0.029 |
| decline | Strong Synchrony | 2 | 0.1 | 0.000 | 0.001 | -0.346 | 0.051 |
| decline | Strong Synchrony | 2 | 0.2 | 0.003 | 0.001 | -0.536 | 0.085 |
| stable | Strong Asynchrony | 0 | 0 | -0.018 | 0.003 | -0.346 | 0.038 |
| stable | Strong Asynchrony | 0 | 0.1 | -0.009 | 0.001 | -0.288 | 0.035 |
| stable | Strong Asynchrony | 0 | 0.2 | -0.004 | 0.001 | -0.376 | 0.051 |
| stable | Strong Asynchrony | 1 | 0 | -0.005 | 0.001 | -0.365 | 0.045 |
| stable | Strong Asynchrony | 1 | 0.1 | -0.005 | 0.001 | -0.429 | 0.051 |
| stable | Strong Asynchrony | 1 | 0.2 | -0.009 | 0.002 | -0.509 | 0.068 |
| stable | Strong Asynchrony | 2 | 0 | -0.007 | 0.001 | -0.355 | 0.038 |
| stable | Strong Asynchrony | 2 | 0.1 | 0.005 | 0.001 | -0.395 | 0.045 |
| stable | Strong Asynchrony | 2 | 0.2 | 0.004 | 0.001 | -0.500 | 0.059 |
| stable | Weak Asynchrony | 0 | 0 | -0.024 | 0.003 | -0.250 | 0.029 |
| stable | Weak Asynchrony | 0 | 0.1 | -0.010 | 0.001 | -0.193 | 0.025 |
| stable | Weak Asynchrony | 0 | 0.2 | -0.005 | 0.001 | -0.209 | 0.028 |
| stable | Weak Asynchrony | 1 | 0 | -0.010 | 0.002 | -0.255 | 0.031 |
| stable | Weak Asynchrony | 1 | 0.1 | -0.007 | 0.001 | -0.300 | 0.034 |
| stable | Weak Asynchrony | 1 | 0.2 | -0.009 | 0.001 | -0.325 | 0.038 |
| stable | Weak Asynchrony | 2 | 0 | -0.020 | 0.003 | -0.252 | 0.029 |
| stable | Weak Asynchrony | 2 | 0.1 | -0.005 | 0.001 | -0.260 | 0.031 |
| stable | Weak Asynchrony | 2 | 0.2 | -0.002 | 0.000 | -0.299 | 0.035 |
| stable | Weak Synchrony | 0 | 0 | -0.014 | 0.002 | -0.206 | 0.025 |
| stable | Weak Synchrony | 0 | 0.1 | -0.005 | 0.001 | -0.222 | 0.027 |
| stable | Weak Synchrony | 0 | 0.2 | -0.003 | 0.001 | -0.240 | 0.030 |
| stable | Weak Synchrony | 1 | 0 | -0.013 | 0.002 | -0.209 | 0.026 |
| stable | Weak Synchrony | 1 | 0.1 | -0.005 | 0.001 | -0.215 | 0.026 |
| stable | Weak Synchrony | 1 | 0.2 | -0.002 | 0.001 | -0.238 | 0.028 |
| stable | Weak Synchrony | 2 | 0 | -0.014 | 0.002 | -0.204 | 0.025 |
| stable | Weak Synchrony | 2 | 0.1 | -0.003 | 0.001 | -0.184 | 0.021 |
| stable | Weak Synchrony | 2 | 0.2 | -0.003 | 0.001 | -0.197 | 0.024 |
| stable | Strong Synchrony | 0 | 0 | -0.015 | 0.002 | -0.205 | 0.025 |
| stable | Strong Synchrony | 0 | 0.1 | -0.005 | 0.001 | -0.317 | 0.042 |
| stable | Strong Synchrony | 0 | 0.2 | -0.003 | 0.000 | -0.469 | 0.058 |
| stable | Strong Synchrony | 1 | 0 | -0.008 | 0.002 | -0.231 | 0.029 |
| stable | Strong Synchrony | 1 | 0.1 | 0.000 | 0.000 | -0.342 | 0.043 |
| stable | Strong Synchrony | 1 | 0.2 | -0.012 | 0.002 | -0.476 | 0.061 |
| stable | Strong Synchrony | 2 | 0 | -0.011 | 0.002 | -0.222 | 0.025 |
| stable | Strong Synchrony | 2 | 0.1 | 0.001 | 0.001 | -0.271 | 0.034 |
| stable | Strong Synchrony | 2 | 0.2 | 0.004 | 0.001 | -0.413 | 0.053 |
| growth | Strong Asynchrony | 0 | 0 | -0.030 | 0.004 | -0.335 | 0.037 |
| growth | Strong Asynchrony | 0 | 0.1 | -0.020 | 0.002 | -0.274 | 0.033 |
| growth | Strong Asynchrony | 0 | 0.2 | -0.022 | 0.002 | -0.357 | 0.044 |
| growth | Strong Asynchrony | 1 | 0 | -0.022 | 0.003 | -0.369 | 0.042 |
| growth | Strong Asynchrony | 1 | 0.1 | -0.018 | 0.003 | -0.436 | 0.049 |
| growth | Strong Asynchrony | 1 | 0.2 | -0.026 | 0.003 | -0.505 | 0.062 |
| growth | Strong Asynchrony | 2 | 0 | -0.021 | 0.003 | -0.352 | 0.038 |
| growth | Strong Asynchrony | 2 | 0.1 | -0.010 | 0.001 | -0.398 | 0.044 |
| growth | Strong Asynchrony | 2 | 0.2 | -0.004 | 0.001 | -0.502 | 0.055 |
| growth | Weak Asynchrony | 0 | 0 | -0.029 | 0.004 | -0.259 | 0.030 |
| growth | Weak Asynchrony | 0 | 0.1 | -0.017 | 0.002 | -0.192 | 0.024 |
| growth | Weak Asynchrony | 0 | 0.2 | -0.021 | 0.002 | -0.210 | 0.027 |
| growth | Weak Asynchrony | 1 | 0 | -0.024 | 0.003 | -0.264 | 0.031 |
| growth | Weak Asynchrony | 1 | 0.1 | -0.018 | 0.002 | -0.304 | 0.034 |
| growth | Weak Asynchrony | 1 | 0.2 | -0.024 | 0.003 | -0.333 | 0.038 |
| growth | Weak Asynchrony | 2 | 0 | -0.027 | 0.003 | -0.263 | 0.030 |
| growth | Weak Asynchrony | 2 | 0.1 | -0.016 | 0.002 | -0.263 | 0.031 |
| growth | Weak Asynchrony | 2 | 0.2 | -0.015 | 0.002 | -0.297 | 0.035 |
| growth | Weak Synchrony | 0 | 0 | -0.012 | 0.002 | -0.215 | 0.026 |
| growth | Weak Synchrony | 0 | 0.1 | -0.005 | 0.001 | -0.229 | 0.027 |
| growth | Weak Synchrony | 0 | 0.2 | -0.004 | 0.001 | -0.248 | 0.030 |
| growth | Weak Synchrony | 1 | 0 | -0.009 | 0.002 | -0.218 | 0.026 |
| growth | Weak Synchrony | 1 | 0.1 | -0.004 | 0.001 | -0.222 | 0.026 |
| growth | Weak Synchrony | 1 | 0.2 | -0.002 | 0.001 | -0.242 | 0.029 |
| growth | Weak Synchrony | 2 | 0 | -0.009 | 0.002 | -0.215 | 0.026 |
| growth | Weak Synchrony | 2 | 0.1 | -0.003 | 0.001 | -0.183 | 0.022 |
| growth | Weak Synchrony | 2 | 0.2 | 0.002 | 0.002 | -0.207 | 0.025 |
| growth | Strong Synchrony | 0 | 0 | -0.011 | 0.002 | -0.215 | 0.026 |
| growth | Strong Synchrony | 0 | 0.1 | -0.003 | 0.001 | -0.263 | 0.033 |
| growth | Strong Synchrony | 0 | 0.2 | -0.003 | 0.001 | -0.364 | 0.045 |
| growth | Strong Synchrony | 1 | 0 | -0.006 | 0.001 | -0.229 | 0.029 |
| growth | Strong Synchrony | 1 | 0.1 | 0.004 | 0.001 | -0.282 | 0.034 |
| growth | Strong Synchrony | 1 | 0.2 | -0.002 | 0.001 | -0.391 | 0.046 |
| growth | Strong Synchrony | 2 | 0 | -0.011 | 0.002 | -0.221 | 0.025 |
| growth | Strong Synchrony | 2 | 0.1 | 0.004 | 0.001 | -0.230 | 0.027 |
| growth | Strong Synchrony | 2 | 0.2 | 0.006 | 0.001 | -0.319 | 0.038 |
| direction | interaction | Lag | Process_error | true_within_rlpiCI | n | perc |
|---|---|---|---|---|---|---|
| decline | Strong Asynchrony | 0 | 0 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 1 | 0 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 1 | 0.1 | Success | 9 | 0.8181818 |
| decline | Strong Asynchrony | 1 | 0.2 | Success | 8 | 0.7272727 |
| decline | Strong Asynchrony | 2 | 0 | Success | 11 | 1.0000000 |
| decline | Strong Asynchrony | 2 | 0.1 | Success | 8 | 0.7272727 |
| decline | Strong Asynchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 0 | 0 | Success | 4 | 0.3636364 |
| decline | Weak Asynchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 1 | 0 | Success | 8 | 0.7272727 |
| decline | Weak Asynchrony | 1 | 0.1 | Success | 9 | 0.8181818 |
| decline | Weak Asynchrony | 1 | 0.2 | Success | 6 | 0.5454545 |
| decline | Weak Asynchrony | 2 | 0 | Success | 5 | 0.4545455 |
| decline | Weak Asynchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| decline | Weak Asynchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 0 | 0 | Success | 7 | 0.6363636 |
| decline | Weak Synchrony | 0 | 0.1 | Success | 8 | 0.7272727 |
| decline | Weak Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 1 | 0 | Success | 10 | 0.9090909 |
| decline | Weak Synchrony | 1 | 0.1 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 1 | 0.2 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 2 | 0 | Success | 8 | 0.7272727 |
| decline | Weak Synchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| decline | Weak Synchrony | 2 | 0.2 | Success | 10 | 0.9090909 |
| decline | Strong Synchrony | 0 | 0 | Success | 8 | 0.7272727 |
| decline | Strong Synchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 1 | 0 | Success | 10 | 0.9090909 |
| decline | Strong Synchrony | 1 | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 1 | 0.2 | Success | 4 | 0.3636364 |
| decline | Strong Synchrony | 2 | 0 | Success | 10 | 0.9090909 |
| decline | Strong Synchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| decline | Strong Synchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 0 | 0 | Success | 4 | 0.3636364 |
| stable | Strong Asynchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 1 | 0 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 1 | 0.1 | Success | 9 | 0.8181818 |
| stable | Strong Asynchrony | 1 | 0.2 | Success | 7 | 0.6363636 |
| stable | Strong Asynchrony | 2 | 0 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| stable | Strong Asynchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 0 | 0 | Success | 3 | 0.2727273 |
| stable | Weak Asynchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 1 | 0 | Success | 6 | 0.5454545 |
| stable | Weak Asynchrony | 1 | 0.1 | Success | 7 | 0.6363636 |
| stable | Weak Asynchrony | 1 | 0.2 | Success | 6 | 0.5454545 |
| stable | Weak Asynchrony | 2 | 0 | Success | 3 | 0.2727273 |
| stable | Weak Asynchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| stable | Weak Asynchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Synchrony | 0 | 0 | Success | 6 | 0.5454545 |
| stable | Weak Synchrony | 0 | 0.1 | Success | 7 | 0.6363636 |
| stable | Weak Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Synchrony | 1 | 0 | Success | 6 | 0.5454545 |
| stable | Weak Synchrony | 1 | 0.1 | Success | 7 | 0.6363636 |
| stable | Weak Synchrony | 1 | 0.2 | Success | 11 | 1.0000000 |
| stable | Weak Synchrony | 2 | 0 | Success | 6 | 0.5454545 |
| stable | Weak Synchrony | 2 | 0.1 | Success | 10 | 0.9090909 |
| stable | Weak Synchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Synchrony | 0 | 0 | Success | 6 | 0.5454545 |
| stable | Strong Synchrony | 0 | 0.1 | Success | 8 | 0.7272727 |
| stable | Strong Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| stable | Strong Synchrony | 1 | 0 | Success | 8 | 0.7272727 |
| stable | Strong Synchrony | 1 | 0.1 | Success | 11 | 1.0000000 |
| stable | Strong Synchrony | 1 | 0.2 | Success | 2 | 0.1818182 |
| stable | Strong Synchrony | 2 | 0 | Success | 6 | 0.5454545 |
| stable | Strong Synchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| stable | Strong Synchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 0 | 0 | Success | 4 | 0.3636364 |
| growth | Strong Asynchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 1 | 0 | Success | 4 | 0.3636364 |
| growth | Strong Asynchrony | 1 | 0.1 | Success | 6 | 0.5454545 |
| growth | Strong Asynchrony | 1 | 0.2 | Success | 5 | 0.4545455 |
| growth | Strong Asynchrony | 2 | 0 | Success | 8 | 0.7272727 |
| growth | Strong Asynchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Asynchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| growth | Weak Asynchrony | 0 | 0 | Success | 3 | 0.2727273 |
| growth | Weak Asynchrony | 0 | 0.1 | Success | 9 | 0.8181818 |
| growth | Weak Asynchrony | 0 | 0.2 | Success | 7 | 0.6363636 |
| growth | Weak Asynchrony | 1 | 0 | Success | 4 | 0.3636364 |
| growth | Weak Asynchrony | 1 | 0.1 | Success | 5 | 0.4545455 |
| growth | Weak Asynchrony | 1 | 0.2 | Success | 3 | 0.2727273 |
| growth | Weak Asynchrony | 2 | 0 | Success | 4 | 0.3636364 |
| growth | Weak Asynchrony | 2 | 0.1 | Success | 8 | 0.7272727 |
| growth | Weak Asynchrony | 2 | 0.2 | Success | 9 | 0.8181818 |
| growth | Weak Synchrony | 0 | 0 | Success | 8 | 0.7272727 |
| growth | Weak Synchrony | 0 | 0.1 | Success | 10 | 0.9090909 |
| growth | Weak Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| growth | Weak Synchrony | 1 | 0 | Success | 11 | 1.0000000 |
| growth | Weak Synchrony | 1 | 0.1 | Success | 11 | 1.0000000 |
| growth | Weak Synchrony | 1 | 0.2 | Success | 11 | 1.0000000 |
| growth | Weak Synchrony | 2 | 0 | Success | 10 | 0.9090909 |
| growth | Weak Synchrony | 2 | 0.1 | Success | 10 | 0.9090909 |
| growth | Weak Synchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 0 | 0 | Success | 8 | 0.7272727 |
| growth | Strong Synchrony | 0 | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 0 | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 1 | 0 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 1 | 0.1 | Success | 9 | 0.8181818 |
| growth | Strong Synchrony | 1 | 0.2 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 2 | 0 | Success | 8 | 0.7272727 |
| growth | Strong Synchrony | 2 | 0.1 | Success | 11 | 1.0000000 |
| growth | Strong Synchrony | 2 | 0.2 | Success | 11 | 1.0000000 |
Expectation: in each case, the width of the CI should increase with process error. The width should also increase when there is strong asynchrony or synchrony.
Not really…